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Probability "With Replacement"

A fireworks warehouse stores 500 bottle rockets, of which 40 are assumed to be duds (meaning that they wouldn't fire if lighted).

If 10 bottle rockets are randomly selected with replacement, then what is the probability that 5 of those selected are duds (to four decimal places)?

(I've been told that the answer is 0.0005 but I'm not sure how to get this answer, someone please help!!)
Original post by SP1234321
A fireworks warehouse stores 500 bottle rockets, of which 40 are assumed to be duds (meaning that they wouldn't fire if lighted).

If 10 bottle rockets are randomly selected with replacement, then what is the probability that 5 of those selected are duds (to four decimal places)?

(I've been told that the answer is 0.0005 but I'm not sure how to get this answer, someone please help!!)


It's hard because you can't do it directly, since you don't know which 5 are to be duds. What you need to spot is that if XX is the number of bottle rockets that are duds out of the 10 selected, then XX has a binomial distribution (with parameters that you should determine). So can you now find the answer P(X=5)P(X=5)?
Reply 2
Avatar for Franzen
Franzen
16
"With replacement" just means that once a rocket is taken from the population and recorded, it is then replaced by an identical rocket (or it's put back if you prefer). So the total population remains at 500 instead of decreasing.

Does that help?

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